%0 Journal Article
%T On the group theoretical background of assigning stepwise mutations onto phylogenies
%A Fischer Mareike
%A Klaere Steffen
%A Thi Nguyen Minh Anh
%A Haeseler Arndt von
%J Algorithms for Molecular Biology
%D 2012
%I BioMed Central
%R 10.1186/1748-7188-7-36
%X Recently one step mutation matrices were introduced to model the impact of substitutions on arbitrary branches of a phylogenetic tree on an alignment site. This concept works nicely for the four-state nucleotide alphabet and provides an efficient procedure conjectured to compute the minimal number of substitutions needed to transform one alignment site into another. The present paper delivers a proof of the validity of this algorithm. Moreover, we provide several mathematical insights into the generalization of the OSM matrix to multi-state alphabets. The construction of the OSM matrix is only possible if the matrices representing the substitution types acting on the character states and the identity matrix form a commutative group with respect to matrix multiplication. We illustrate this approach by looking at Abelian groups over twenty states and critically discuss their biological usefulness when investigating amino acids.
%K Maximum likelihood
%K Maximum parsimony
%K Substitution model
%K Tree reconstruction
%K Group theory
%U http://www.almob.org/content